Pith Number

pith:UQPH7MXH

pith:2012:UQPH7MXHUTOKZG67VPLYAV36TY

not attested not anchored not stored refs pending

Anatomy of the giant component: The strictly supercritical regime

Eyal Lubetzky, Jian Ding, Yuval Peres

arxiv:1202.6112 v1 · 2012-02-28 · math.CO · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UQPH7MXHUTOKZG67VPLYAV36TY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:00:00.737256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a41e7fb2e7a4dcac9bdfabd780577e9e0e977bef62a37b63b25111f641c4afa1

Aliases

arxiv: 1202.6112 · arxiv_version: 1202.6112v1 · doi: 10.48550/arxiv.1202.6112 · pith_short_12: UQPH7MXHUTOK · pith_short_16: UQPH7MXHUTOKZG67 · pith_short_8: UQPH7MXH

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UQPH7MXHUTOKZG67VPLYAV36TY \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a41e7fb2e7a4dcac9bdfabd780577e9e0e977bef62a37b63b25111f641c4afa1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ec6f6d730c90c8a8186975d66778ba34b1c9a597b54ac3884acf207d0da02fe",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-02-28T04:09:03Z",
    "title_canon_sha256": "e4aad695b28f395ef36f16dbbae63f8747ba69a43104700633611cb038e0a057"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.6112",
    "kind": "arxiv",
    "version": 1
  }
}